Computational Techniques for Fluid Dynamics: Fundamental and general techniques
The purpose of this textbook is to provide senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques, that have proven effective in the various brances of computational fluid dynamics.
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Partial Differential Equations
Preliminary Computational Techniques
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accuracy algebraic equations applied approximate factorisation approximate solution approximating functions BANFAC BANSOL Burgers Chap coefficients computational domain convection equation convective convective terms Crank-Nicolson finite Crank-Nicolson scheme diffusion equation dimensions Dirichlet boundary conditions discretised equations dissipation eigenvalues equation Sect equivalent evaluated exact solution explicit finite difference method finite element method finite volume method fluid dynamics FORMATC four-point upwind Fourier FTCS scheme Galerkin finite element generalised governing equations grid points higher-order IF(ME EQ implemented implicit schemes initial conditions introduced Listing of program mass operator matrix method Sect modified equation Neumann boundary conditions Neumann stability analysis Newton's method node nonlinear number of iterations one-dimensional parameter partial differential equation produces rms error second-order shown in Fig shown in Table solution error solved spectral method subroutine system of equations Taylor series techniques Thomas algorithm three-level three-point time-level time-step transport equation tridiagonal system truncation error two-dimensional upwind scheme wavelengths